We show that as an electron transfers between closed-shellmolecular fragments at large separation,
the exact correlation potential of time-dependent density functional theory gradually develops a step
and peak structure in the bonding region. This structure has a density-dependence that is non-local
both in space and time, and even the exact ground-state exchange-correlation functional fails to capture
it. In the complementary case of charge-transfer between open-shell fragments, an initial step
and peak vanish as the charge-transfer state is reached. Lack of these structures in usual approximations
leads to inaccurate charge-transfer dynamics. This is dramatically illustrated by the complete
lack of Rabi oscillations in the dipole moment under conditions of resonant charge-transfer.